Question

A bar magnet of magnetic moment $M$ is cut into parts of equal lengths. The magnetic moment and pole strength of either part is
A. $M/2,m/2$
B. $M,m/2$
C. $M/2,m$
D. $M,m$

Answer 1

Use the formula for magnetic moment of a bar magnet. This formula gives the relation between the pole strength of the magnet and distance between the poles of the bar magnet. Recall the basics of pole strength of a magnet and check whether the pole strength changes after cutting it. Then determine the new length of the cut pieces of the magnet and determine the new magnetic moment of the either cut pieces.

Formula used:
The magnetic moment $M$ of a bar magnet is given by
$M = m \times 2l$ …… (1)
Here, $m$ is the pole strength of the bar magnet and $2l$ is the length between the two poles of the bar magnet.

Complete step by step answer:
We have given that the magnetic moment of a bar magnet is $M$. This bar magnet is cut into two pieces of equal lengths.We have asked to determine the magnetic moment and pole strength of these cut pieces of magnet.The pole strength of a magnet is the strength by which the poles of a magnet can attract the magnetic materials towards itself.

When the bar magnet is cut into two equal pieces of the same length, the new cut pieces of the bar magnet again form the magnetic poles at its ends and behave as a magnet. The strength of the magnetic poles of the new magnets remains the same though it is cut into pieces.Hence, the pole strength of the magnet remains the same.

Let us now determine the magnetic moment of the cut pieces of the magnet.When the magnet is cut, the distance between the poles of the magnet halves to original value.The initial magnetic moment of the magnet is given by
$M = m \times 2l$
The magnetic moment of the two magnets is given by
$M' = m \times l$
$\Rightarrow M' = \dfrac{M}{2}$
Thus, the magnetic moment of the bar magnets is $\dfrac{M}{2}$.Hence, the new magnetic moment and pole strength of the magnets are $\dfrac{M}{2}$ and $m$ respectively.

Hence, the correct option is C.

Note: The students should keep in mind that we have determined the values of the magnetic moment and pole strength of the cut pieces of the magnet assuming that the magnet is cut perpendicular to its axis. If the magnetic is cut along any other axis or plane then the values of the magnetic moment and pole strength may be different.